#900 ⟨a, b | aaabaaa=bb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. b3a3 ⇒ a3b3 [2]
2. a3ba3 ⇒ b2 [1]
3. b2aba3 ⇒ a3bab2 [3]
4. b2a2ba3 ⇒ a3ba2b2 [4]
# ab:aaabaaa=bb ab
bbbaaa=aaabbb
aaabaaa=bb
bbabaaa=aaababb
bbaabaaa=aaabaabb

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
9776⟨a, b | aaabbaaa=b⟩Infinite cancellative non-commutative monoid
101624⟨a, b | aaababaaa=b⟩Infinite cancellative non-commutative monoid
102157⟨a, b | aaabaaa=bab⟩Infinite cancellative non-commutative monoid
113442⟨a, b | aaabaabaaa=b⟩Infinite cancellative non-commutative monoid
115018⟨a, b | aaabaaa=baab⟩Infinite cancellative non-commutative monoid